SOCP (Second-Order Cone Programming)

Second-Order Cone Programming (SOCP) is a type of mathematical optimization used to find the best solution within specific constraints. It involves optimizing a linear function while ensuring that certain variables satisfy second-order (or Lorentz) cone conditions—geometric shapes resembling ice-cream cones. These conditions often represent relationships like inequalities involving Euclidean norms. SOCP is powerful because it can model a wide range of problems in engineering, finance, and machine learning, allowing efficient and reliable solutions even in complex scenarios involving uncertainty or nonlinear relationships.